\[ \int \frac {1}{\left (c (a+b x)^2\right )^{5/2}} \, dx \]
Optimal antiderivative \[ -\frac {1}{4 b \,c^{2} \left (b x +a \right )^{3} \sqrt {c \left (b x +a \right )^{2}}} \]
command
integrate(1/(c*(b*x+a)^2)^(5/2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ -\frac {1}{4 \, {\left (b x + a\right )}^{4} b c^{\frac {5}{2}} \mathrm {sgn}\left (b x + a\right )} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \mathit {sage}_{0} x \]________________________________________________________________________________________